# American Institute of Mathematical Sciences

doi: 10.3934/era.2020086

## Some properties for almost cellular algebras

 1 School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China 2 Department of Mathematics, Shanghai University, Shanghai 200444, China

* Corresponding author: Nan Gao

Received  April 2020 Revised  June 2020 Published  August 2020

Fund Project: The first author is supported by National Natural Science Foundation of China Project (No. 11901146), and the second author is supported by National Natural Science Foundation of China Project (No.11771272)

In this paper, we will investigate some properties for almost cellular algebras. We compare the almost cellular algebras with quasi-hereditary algebras, which are known to carry any homological and categorical structures. We prove that any almost cellular algebra is the iterated inflation and obtain some sufficient and necessary conditions for an almost cellular algebra $\mathrm{A}$ to be quasi-hereditary.

Citation: Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, doi: 10.3934/era.2020086
##### References:

show all references

##### References:
 [1] Wenjun Liu, Yukun Xiao, Xiaoqing Yue. Classification of finite irreducible conformal modules over Lie conformal algebra $\mathcal{W}(a, b, r)$. Electronic Research Archive, , () : -. doi: 10.3934/era.2020123 [2] Guido Cavallaro, Roberto Garra, Carlo Marchioro. Long time localization of modified surface quasi-geostrophic equations. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020336 [3] Marion Darbas, Jérémy Heleine, Stephanie Lohrengel. Numerical resolution by the quasi-reversibility method of a data completion problem for Maxwell's equations. Inverse Problems & Imaging, 2020, 14 (6) : 1107-1133. doi: 10.3934/ipi.2020056 [4] Wenmeng Geng, Kai Tao. Large deviation theorems for dirichlet determinants of analytic quasi-periodic jacobi operators with Brjuno-Rüssmann frequency. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5305-5335. doi: 10.3934/cpaa.2020240 [5] Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $L^2-$norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077